Solution of the population balance equation for wet granulation using second kind Chebyshev polynomials

Wet granulation is used in many industrial fields, such as pharmaceutical and nutraceutical, to improve compressibility properties of powders. The comprehension of the physical phenomena of the granulation process, such as simultaneous particle breakage, aggregation, and nucleation, is fundamental to optimize the operating conditions. In this work the population balance equation (PBE), used to mathematically describe these physical phenomena, has been numerical solved with a new finite element method with expansion coefficients in terms of a truncated series expansion with the orthogonal second kind Chebyshev basis polynomials. Such a numerical method is a straightforward and effective method, which has the advantage of concurrently giving the distribution and the different required moments. Moreover, the proposed model accounting for the breakage, aggregation, and nucleation phenomena was used in an ad-hoc optimization procedure to describe the particle size distribution of experimental results of a wet granulation process reaching satisfactorily RMS values.